Monday, 31 October 2011

Wednesday, 26 October 2011

Suppose you run a study to compare two groups of children:
say a dyslexic group and a control group. Your favourite theory predicts a
difference in auditory perception, but you find no difference between the
groups. What to do? You may feel a further study is needed: perhaps there were
floor or ceiling effects that masked true differences. Maybe you need more
participants to detect a small effect. But what if you can’t find flaws in the
study and decide to publish the result? You’re likely to hit problems. Quite
simply, null results are much harder to publish than positive findings. In
effect, you are telling the world “Here’s an interesting theory that could
explain dyslexia, but it’s wrong.” It’s not exactly an inspirational message,
unless the theory is so prominent and well-accepted that the null finding is surprising.
And if that is the case, then it’s unlikely that your single study is going to
be convincing enough to topple the status quo. It has been recognised for years
that this “file drawer problem” leads to distortion of the research literature,
creating an impression that positive results are far more robust than they
really are (Rosenthal, 1979).

The medical profession has become aware of the issue and
it’s now becoming common practice for clinical trials to be registered before a
study commences, and for journals to undertake to publish the results of
methodologically strong studies regardless of outcome. In the past couple of
years, two early-intervention studies with null results have been published, on
autism (Green et al, 2010) and late talkers (Wake et al, 2011). Neither study
creates a feel-good sensation: it’s disappointing that so much effort and good
intentions failed to make a difference. But it’s important to know that, to
avoid raising false hopes and wasting scarce resources on things that aren’t
effective. Yet it’s unlikely that either study would have found space in a
high-impact journal in the days before trial registration.

Registration can also exert an important influence in cases
where conflict of interest or other factors make researchers reluctant to
publish null results. For instance, in 2007, Cylharova et al published a study
relating membrane fatty acid levels to dyslexia in adults. This research group
has a particular interest in fatty acids and neurodevelopmental disabilities,
and the senior author has written a book on this topic. The researchers
argued that the balance of omega 3 and omega 6 fatty acids differed between
dyslexics and non-dyslexics, and concluded: “To gain a more precise understanding of the effects of omega-3 HUFA
treatment, the results of this study need to be confirmed by blood biochemical
analysis before and after supplementation”. They further stated that a
randomised controlled trial was underway. Yet four years later, no results have
been published and requests for information about the findings are met with
silence. If the trial had been registered, the authors would have been required
to report the results, or explain why they could not do so.

Advance registration of research is not a feasible option
for most areas of psychology, so what steps can we take to reduce publication
bias? Many years ago a wise journal editor told me that publication decisions
should be based on evaluation of just the Introduction and Methods sections of
a paper: if an interesting hypothesis had been identified, and the methods were
appropriate to test it, then the paper should be published, regardless of the
results.

People often respond to this idea saying that it would just
mean the literature would be full of boring stuff. But remember, I'm not suggesting that any old rubbish should get published: there has to be a good case for doing the study made in the Introduction, and the Methods have to be strong. Also, some kinds of boring results are important: miminally, publication of a null result may save some hapless
graduate student from spending three years trying to demonstrate an effect
that’s not there. Estimates of effect sizes in meta-analyses are compromised if
only positive findings get reported. More seriously, if we are talking about
research with clinical implications, then over-estimation of effects can lead
to inappropriate interventions being adopted.

Things are slowly changing and it’s getting easier to
publish null results. The advent of electronic journals has made a big
difference because there is no longer such pressure on page space. The
electronic journal PLOS One adopts a publication policy that is pretty close to
that proposed by the wise editor: they state they will publish all papers that
are technically sound. So my advice to those of you who have null data from
well-designed experiments languishing in that file drawer: get your findings
out there in the public domain.

The DfE report paints a dire picture: “GCSE pupils' reading
is more than a year behind the standard of their peers in Shanghai, Korea and
Finland….Fifteen-year-olds in England are also at least six months behind those
in Hong Kong, Singapore, Canada, New Zealand, Japan and Australia, according to
the Department for Education's (DfE) analysis of the OECD's 2009 Programme for
International Student Assessment (PISA) study.” The report goes on to talk of England
slipping behind other nations in reading.

Schools Minister Nick Gibb is quoted as saying: “The gulf
between our 15-year-olds' reading abilities and those from other countries is
stark – a gap that starts to open in the very first few years of a child's education.”

I started to smell a rat when I looked at a chart in the
report, entitled “Attainment gap between England
and the countries performing
significantly better than England”
(my emphasis). This seemed an odd kind of chart to provide if one wanted to
evaluate how England
is doing compared to other countries. So I turned to the report
provided by the people who did the survey.

Here are some salient points taken verbatim from their
summary on reading:

Twelve countries had mean scores for
reading which were significantly higher than that of England. In 14 countries the
difference in mean scores from that in England was not statistically
significant. Thirty-eight countries had mean scores that were
significantly lower than England.

The mean score for reading in England
was slightly above the OECD average but this difference was not
statistically significant.

England’s performance in 2009 does not differ
greatly from that in the last PISA
survey in 2006.

There is, of course, no problem with aiming high and wanting
our children to be among the top achievers in the world. But that’s no excuse
for the DfE's mendacious manipulation of information.

Wednesday, 5 October 2011

Have I gone over to the dark side? Cracked under pressure
from the REF to resort to fabrication of results to secure that elusive Nature
paper? Or had my brain addled by so many requests for information from ethics
committees that I’ve just decided that its easier to be unethical? Well readers
will be reassured to hear that none of these things is true. What I have to say
concerns the benefits of made-up data for helping understand how to analyse
real data.

In my field of experimental psychology, students get a
thorough grounding in statistics and learn how to apply various methods for
testing whether groups differ from one another, whether variables are
associated and so on. But what they typically don’t get is any instruction in
how to simulate datasets. This may be a historical hangover. When I first
started out in the field, people didn’t have their own computers, and if you
wanted to do an analysis you either laboriously assembled a set of instructions
in Fortran which were punched onto cards and run on a mainframe computer
(overnight if you were lucky), or you did the sums on a pocket calculator. Data
simulation was just unfeasible for most people. Over the years, the
landscape has changed beyond recognition and there are now windows-based
applications that allow one to do complex multivariate statistics at the press
of a button. There is a danger, however, which is that people do analyses
without understanding them. And one of the biggest problems of all is a
tendency to apply statistical analyses post hoc. You can tell people over and
over that this is a Bad Thing (see Gould and Hardin, 2003) but they just don’t get it. A little simulation
exercise can be worth a thousand words.

So here’s an illustration. Suppose we’ve got two groups each
of 10 people, let’s say left-handers and right-handers. And we’ve given them a
battery of 20 cognitive tests. When we scrutinise the results, we find that
they don’t differ on most of the measures, but there’s a test of mathematical
skill on which the left-handers outperform the right-handers. We do a t-test
and are delighted to find that on this measure, the difference between groups is
significant at the .05 level, so we write up a paper entitled "Left-handed advantage for mathematical skills" and submit it to a
learned journal, not mentioning the other 19 tests. After all, they weren’t
very interesting. Sounds OK? Well, it isn’t. We have fallen into the trap of using statistical methods that are valid
for testing a hypothesis that is specified a priori in a situation where the
hypothesis only emerged after scrutinising the data.

Let’s generate some data. Most people have access to
Microsoft Excel, which is perfect for simple simulations. In row 1 we put our
column labels, which are group, var1, var2, …. var 20.

In column A, we then have ten zeroes followed by ten ones, indicating group identity.
We then use random numbers to complete the table. The simplest way to do this
is to just type in each cell:

=RAND()

This generates a random number between 0 and 1.

A more sophisticated option is to generate a random z-score.
This creates random numbers that meet the assumption of many statistical tests
that data are normally distributed. You do this by typing:

=NORMSINV(RAND())

At the foot of each column you can compute the mean and
standard deviation for each group, and Excel automatically computes a p-value
based on the t-test for comparing the groups with a command such as:

So the formulae in the first three columns look like this (rows 4-20 are hidden):

Copy this formula across all columns. I added conditional formatting
to row 27 so that ‘significant’ p-values are highlighted in yellow (and it
just so happens with this example that the generated data gave a p-value
less than .05 for column C).

Every time you type anything at all on the sheet, all the
random numbers are updated: I’ve just added a row called ‘thisrun’ and typing any number in cell B29 will re-run the simulation. This provides a simple way of generating a
series of simulations and seeing when p-values fall below .05. On some runs,
all the t-tests are nonsignificant, but you’ll quickly see that on many runs
one or more p-values are below .05. In fact, on average, across numerous runs,
the average number of significant values is going to be one because we have twenty columns, and 1/20 = .05. That’s what p <
.05 means! If this doesn’t convince you of the importance of specifying your
hypothesis in advance, rather than selecting data for analysis post hoc,
nothing will.

This is a very simple example, but you can extend the
approach to much more complicated analytic methods. It gets challenging in
Excel if you want to generate correlated variables, though if you type a
correlation coefficient in cell A1, and have a random number in column B, and
copy this formula down from cell C2, then columns B and C will be correlated by
the value in cell A1:

=B2*A$1+NORMSINV(RAND())*SQRT(1-A$1^2)

NB, you won’t get the exact correlation on each run: the
precision will increase with the number of rows you simulate.

Other applications, such as Matlab or R, allow you to
generate correlated data more easily. There are examples of simulating multivariate normal datasets in R in my blog on twin methods.

Simulation can be used not just for exploring a whole host
of issues around statistical methods. For instance, you can simulate data to
see how sample size affects results, or how results change if you fail to meet
assumptions of a method. But overall, my message is that data simulation is a
simple and informative approach to gaining understanding of statistical
analysis. It should be used much more widely in training students.